Chapter 11, Problem 11B.4ST

Interpretation Introduction

Interpretation:

Frequency and wavelength of the transition $\text{J = 1}\leftarrow \text{0}$ in the molecule ${}^{\text{2}}{\text{H}}^{\text{35}}\text{Cl}$ has to be determined where $m_u\left({}^{2}H\right)=\text{ 2}{\text{.0141m}}_{\text{u}}$. The frequency of ${}^1{\text{H}}^{\text{35}}\text{Cl}$ in the given transition is higher or lower than that of ${}^{\text{2}}{\text{H}}^{\text{35}}\text{Cl}$ has to be decided.

Concept Introduction:

Rotational constant of a molecule can be determined using the given formula.

  $\begin{array}{c}\text{Rotational constant, B = }\frac{\hslash }{\text{4πI}}\\ \\ \text{where,}\\ \text{I = moment of inertia }\end{array}$

Moment of inertia of diatomic molecules is given by,

  $\begin{array}{l}\text{Moment of inertia, I = }\mu {\text{R}}^2\\ \\ where,\mu =\frac{m_A{m}_B}{\left(m_A+m_B\right)}\end{array}$

Rotational transition frequency of the radiation that is absorbed during a transition that starts from the level J is given by,

  ${\nu }_J\text{ = 2B}\left(J+1\right)$

Wavelength and frequency are inversely proportional to each other and can be given as,

  $\begin{array}{c}\text{ν}\text{=}\frac{\text{c}}{\text{λ}}\\ \text{where, ν}=\text{frequency}\\ \text{λ}=\text{wavelength}\\ \text{c = speed of light}\end{array}$